2 technology required. the data represent the amount of corn, in bushels per acre, harvested from different…

Explanation:

Step1: Organize data for dot - plot

Count the frequency of each value in the data set {133, 133, 134, 134, 134, 135, 135, 135, 135, 135, 135, 135, 136, 136, 136, 137, 137, 138, 138, 139, 140} to create a dot - plot. For example, 133 appears 2 times, 134 appears 3 times etc.

Step2: Calculate quartiles for box - plot

1. First, order the data. There are (n = 21) data points.
   • The median ((Q_2)) is the (\left(\frac{n + 1}{2}\right))-th value. So, (\frac{21+1}{2}=11) - th value, which is 135.
   • The lower half of the data has (n_1 = 10) values. The median of the lower half ((Q_1)) is the (\left(\frac{10 + 1}{2}\right)=5.5) - th value. Taking the average of the 5 - th and 6 - th values in the lower half (134 and 135), (Q_1=\frac{134 + 135}{2}=134.5).
   • The upper half of the data has (n_2 = 10) values. The median of the upper half ((Q_3)) is the (\left(5.5+11\right))-th value (counting from the start of the data). Taking the average of the 5 - th and 6 - th values in the upper half (137 and 138), (Q_3=\frac{137+138}{2}=137.5). The minimum is 133 and the maximum is 140. This is used to create the box - plot.

Step3: Determine shape of distribution

Since the data has a single peak around 135 and is relatively symmetric around this value, the shape of the distribution is approximately symmetric.

Step4: Compare dot - plot and box - plot

• The dot - plot shows the exact frequency of each data value, allowing us to see the individual data points and any clustering or gaps in the data.
• The box - plot shows the five - number summary (minimum, (Q_1), (Q_2), (Q_3), maximum), which gives information about the spread and skewness of the data, as well as any potential outliers.

Answer:

a. (Since technology is required to create the plots, specific plots are not shown here. But the steps to create them are above). b. Approximately symmetric. c. The dot - plot shows individual data points and frequencies, while the box - plot shows the five - number summary and spread/skewness information.